Heisenberg groups, semifields, and translation planes

For Heisenberg groups constructed over semifields (i.e., not necessarily associative division rings), we solve the isomorphism problem and determine the automorphism groups. We show that two Heisenberg groups over semifields are isomorphic precisely if the semifields are isotopic or anti-isotopic to...

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Bibliographic Details
Published in:Beiträge zur Algebra und Geometrie 2015-03, Vol.56 (1), p.115-127
Main Authors: Knarr, Norbert, Stroppel, Markus J.
Format: Article
Language:English
Subjects:
Algebra
Algebraic Geometry
Convex and Discrete Geometry
Geometry
Mathematics
Mathematics and Statistics
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Summary:For Heisenberg groups constructed over semifields (i.e., not necessarily associative division rings), we solve the isomorphism problem and determine the automorphism groups. We show that two Heisenberg groups over semifields are isomorphic precisely if the semifields are isotopic or anti-isotopic to each other. This condition means that the corresponding translation planes are isomorphic or dual to each other.
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-014-0193-7